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Math Prof Uncovers Secret Chord
chebucto writes "The opening chord to A Hard Day's Night is famous because for 40 years, no one quite knew exactly what chord Harrison was playing. Musicians, scholars and amateur guitar players alike had all come up with their own theories, but it took a Dalhousie mathematician to figure out the exact formula. Dr. Brown used Fourier transforms to find the notes in the chord, and deduced that another George — George Martin, the Beatles producer — also played on the chord, adding a piano chord that included an F note impossible to play with the other notes on the guitar."
Stories like this are actually interesting and have a math/science side to them, instead of being mindless humor that everyone has already seen elsewhere. This is something that a math teacher could show her students to make them interested, more so than all the silly posters and videos they used when I was going through grade school.
...adding a piano chord that included an F note impossible to play with the other notes on the guitar.
There are no notes that are impossible to play on a guitar. However, you have to tune the guitar to a nonstandard, non eagbde like Led Zepplin did on a few songs (an example is Black Mountain Side on their first album.
I have an incredibly hard time playing a B chord; I have to kind of fake it and not hit all the strings. But then I'm no virtuoso, it took me twenty years to learn Starway To Heaven.
Free Martian Whores!
Graphic equalizers often cheat, actually.
I think the problem is a little more interesting than the story makes it out to be. As you point out, you should be able to recognize the overall chord pretty easily with an FT, but it's not quite as trivial to figure out who's playing what. For that you have to analyze the ratios of the harmonics, which turns into a nasty little decomposition problem when you've got more than one instrument playing the same note.